Modelling discrepancy in Bayesian calibration of reservoir models

Simulation models of physical systems such as oil field reservoirs are subject to numerous uncertainties such as observation errors and inaccurate initial and boundary conditions. However, after accounting for these uncertainties, it is usually observed that the mismatch between the simulator output and the observations remains and the model is still inadequate. This incapability of computer models to reproduce the real-life processes is referred to as model inadequacy. This thesis presents a comprehensive framework for modelling discrepancy in the Bayesian calibration and probabilistic forecasting of reservoir models. The framework efficiently implements data-driven approaches to handle uncertainty caused by ignoring the modelling discrepancy in reservoir predictions using two major hierarchical strategies, parametric and non-parametric hierarchical models. The central focus of this thesis is on an appropriate way of modelling discrepancy and the importance of the model selection in controlling overfitting rather than different solutions to different noise models. The thesis employs a model selection code to obtain the best candidate solutions to the form of non-parametric error models. This enables us to, first, interpolate the error in history period and, second, propagate it towards unseen data (i.e. error generalisation). The error models constructed by inferring parameters of selected models can predict the response variable (e.g. oil rate) at any point in input space (e.g. time) with corresponding generalisation uncertainty. In the real field applications, the error models reliably track down the uncertainty regardless of the type of the sampling method and achieve a better model prediction score compared to the models that ignore discrepancy. All the case studies confirm the enhancement of field variables prediction when the discrepancy is modelled. As for the model parameters, hierarchical error models render less global bias concerning the reference case. However, in the considered case studies, the evidence for better prediction of each of the model parameters by error modelling is inconclusive

Developing tools for determination of parameters involved in CO₂ based EOR methods

To mitigate the effects of climate change, CO₂ reduction strategies are suggested to lower anthropogenic emissions of greenhouse gasses owing to the use of fossil fuels. Consequently, the application of CO₂ based enhanced oil recovery methods (EORs) through petroleum reservoirs turn into the hot topic among the oil and gas researchers. This thesis includes two sections. In the first section, we developed deterministic tools for determination of three parameters which are important in CO₂ injection performance including minimum miscible pressure (MMP), equilibrium ratio (Kᵢ), and a swelling factor of oil in the presence of CO₂. For this purposes, we employed two inverse based methods including gene expression programming (GEP), and least square support vector machine (LSSVM). In the second part, we developed an easy-to-use, cheap, and robust data-driven based proxy model to determine the performance of CO₂ based EOR methods. In this section, we have to determine the input parameters and perform sensitivity analysis on them. Next step is designing the simulation runs and determining the performance of CO₂ injection in terms of technical viewpoint (recovery factor, RF). Finally, using the outputs gained from reservoir simulators and applying LSSVM method, we are going to develop the data-driven based proxy model. The proxy model can be considered as an alternative model to determine the efficiency of CO₂ based EOR methods in oil reservoir when the required experimental data are not available or accessible

ADVANCED REFLECTION SEISMIC STUDIES OF PHASE I WEYBURN CO2 SEQUESTRATION MONITORING

Three-dimensional, time-lapse (TL) reflection seismic datasets and well logs collected for Phase I CO2 sequestration project in Weyburn oilfield (southern Saskatchewan, Canada) are utilized for developing new approaches in three research areas: 1) estimation of seismic source waveforms, 2) evaluation of TL acoustic impedance (AI) variations for monitoring CO2 propagation, and 3) rigorous modeling of seismic waves propagating through finely layered rock. All three study areas are interconnected and important for accurate analysis of seismic data and TL monitoring of this and other oil reservoirs undergoing fluid injection. The first approach focuses on estimating the source waveforms from reflection seismic data, which is critical for evaluating accurate well-to-seismic ties as well as in other applications. A simple and effective method is proposed, based on iterative identification of the strongest and sparse reflections in seismic records, which allows estimation of source waveforms through an optimization approach, without well-log control and statistical hypotheses. The method allows correcting for coherent noise which seems to occur in stacked Weyburn data, consisting in (de)amplification and time shifts of the low-frequency components of the records. The method is tested on real and self-similar synthetic well-log models and applied to the Weyburn seismic data. For the second topic, a post-stack waveform-calibration processing procedure is developed in order to achieve accurate consistency of TL datasets. Time shifts between the monitor and baseline records are also measured during this procedure, and an improved method for calculating the TL reflectivity differences is proposed. Further, instead of subtraction of the baseline and monitor AIs, TL AI variations are evaluated directly from the reflectivity differences and baseline AI. AI inversion is performed by an accurate and stable method using the stacked reflection and well-log data, and also seismic velocities measured during data processing. The inverted time shifts and TL AI variations correlate with CO2 distributions within the reservoir and allow estimating parameters of the reservoir. In the third research area, a completely new approach to seismic wave modeling is proposed. Rigorous first-principle continuum mechanics is used instead of the conventional viscoelastic approximation. This modeling considers the existence of internal variables, body-force internal friction, and boundary conditions for internal variables. These factors are disregarded in the viscoelastic model, but they should cause dominant effects on seismic-wave attenuation and velocity dispersion in layered media. Numerical modeling of seismic wave propagation is performed in a model of the Weyburn Field. The resulting wavefield and seismic attenuation parameters are found to strongly depend on the internal boundary conditions between layers. Several types of quality (Q) factors are measured in the modeled synthetic waveforms

Exploring the adoption of a conceptual data analytics framework for subsurface energy production systems: a study of predictive maintenance, multi-phase flow estimation, and production optimization

Als die Technologie weiter fortschreitet und immer stärker in der Öl- und Gasindustrie integriert wird, steht eine enorme Menge an Daten in verschiedenen Wissenschaftsdisziplinen zur Verfügung, die neue Möglichkeiten bieten, informationsreiche und handlungsorientierte Informationen zu gewinnen. Die Konvergenz der digitalen Transformation mit der Physik des Flüssigkeitsflusses durch poröse Medien und Pipeline hat die Entwicklung und Anwendung von maschinellem Lernen (ML) vorangetrieben, um weiteren Mehrwert aus diesen Daten zu gewinnen. Als Folge hat sich die digitale Transformation und ihre zugehörigen maschinellen Lernanwendungen zu einem neuen Forschungsgebiet entwickelt. Die Transformation von Brownfields in digitale Ölfelder kann bei der Energieproduktion helfen, indem verschiedene Ziele erreicht werden, einschließlich erhöhter betrieblicher Effizienz, Produktionsoptimierung, Zusammenarbeit, Datenintegration, Entscheidungsunterstützung und Workflow-Automatisierung. Diese Arbeit zielt darauf ab, ein Rahmenwerk für diese Anwendungen zu präsentieren, insbesondere durch die Implementierung virtueller Sensoren, Vorhersageanalytik mithilfe von Vorhersagewartung für die Produktionshydraulik-Systeme (mit dem Schwerpunkt auf elektrischen Unterwasserpumpen) und präskriptiven Analytik für die Produktionsoptimierung in Dampf- und Wasserflutprojekten. In Bezug auf virtuelle Messungen ist eine genaue Schätzung von Mehrphasenströmen für die Überwachung und Verbesserung von Produktionsprozessen entscheidend. Diese Studie präsentiert einen datengetriebenen Ansatz zur Berechnung von Mehrphasenströmen mithilfe von Sensormessungen in elektrischen untergetauchten Pumpbrunnen. Es wird eine ausführliche exploratorische Datenanalyse durchgeführt, einschließlich einer Ein Variablen Studie der Zielausgänge (Flüssigkeitsrate und Wasseranteil), einer Mehrvariablen-Studie der Beziehungen zwischen Eingaben und Ausgaben sowie einer Datengruppierung basierend auf Hauptkomponentenprojektionen und Clusteralgorithmen. Feature Priorisierungsexperimente werden durchgeführt, um die einflussreichsten Parameter in der Vorhersage von Fließraten zu identifizieren. Die Modellvergleich erfolgt anhand des mittleren absoluten Fehlers, des mittleren quadratischen Fehlers und des Bestimmtheitskoeffizienten. Die Ergebnisse zeigen, dass die CNN-LSTM-Netzwerkarchitektur besonders effektiv bei der Zeitreihenanalyse von ESP-Sensordaten ist, da die 1D-CNN-Schichten automatisch Merkmale extrahieren und informative Darstellungen von Zeitreihendaten erzeugen können. Anschließend wird in dieser Studie eine Methodik zur Umsetzung von Vorhersagewartungen für künstliche Hebesysteme, insbesondere bei der Wartung von Elektrischen Untergetauchten Pumpen (ESP), vorgestellt. Conventional maintenance practices for ESPs require extensive resources and manpower, and are often initiated through reactive monitoring of multivariate sensor data. Um dieses Problem zu lösen, wird die Verwendung von Hauptkomponentenanalyse (PCA) und Extreme Gradient Boosting Trees (XGBoost) zur Analyse von Echtzeitsensordaten und Vorhersage möglicher Ausfälle in ESPs eingesetzt. PCA wird als unsupervised technique eingesetzt und sein Ausgang wird weiter vom XGBoost-Modell für die Vorhersage des Systemstatus verarbeitet. Das resultierende Vorhersagemodell hat gezeigt, dass es Signale von möglichen Ausfällen bis zu sieben Tagen im Voraus bereitstellen kann, mit einer F1-Bewertung größer als 0,71 im Testset. Diese Studie integriert auch Model-Free Reinforcement Learning (RL) Algorithmen zur Unterstützung bei Entscheidungen im Rahmen der Produktionsoptimierung. Die Aufgabe, die optimalen Injektionsstrategien zu bestimmen, stellt Herausforderungen aufgrund der Komplexität der zugrundeliegenden Dynamik, einschließlich nichtlinearer Formulierung, zeitlicher Variationen und Reservoirstrukturheterogenität. Um diese Herausforderungen zu bewältigen, wurde das Problem als Markov-Entscheidungsprozess reformuliert und RL-Algorithmen wurden eingesetzt, um Handlungen zu bestimmen, die die Produktion optimieren. Die Ergebnisse zeigen, dass der RL-Agent in der Lage war, den Netto-Barwert (NPV) durch kontinuierliche Interaktion mit der Umgebung und iterative Verfeinerung des dynamischen Prozesses über mehrere Episoden signifikant zu verbessern. Dies zeigt das Potenzial von RL-Algorithmen, effektive und effiziente Lösungen für komplexe Optimierungsprobleme im Produktionsbereich zu bieten.As technology continues to advance and become more integrated in the oil and gas industry, a vast amount of data is now prevalent across various scientific disciplines, providing new opportunities to gain insightful and actionable information. The convergence of digital transformation with the physics of fluid flow through porous media and pipelines has driven the advancement and application of machine learning (ML) techniques to extract further value from this data. As a result, digital transformation and its associated machine-learning applications have become a new area of scientific investigation. The transformation of brownfields into digital oilfields can aid in energy production by accomplishing various objectives, including increased operational efficiency, production optimization, collaboration, data integration, decision support, and workflow automation. This work aims to present a framework of these applications, specifically through the implementation of virtual sensing, predictive analytics using predictive maintenance on production hydraulic systems (with a focus on electrical submersible pumps), and prescriptive analytics for production optimization in steam and waterflooding projects. In terms of virtual sensing, the accurate estimation of multi-phase flow rates is crucial for monitoring and improving production processes. This study presents a data-driven approach for calculating multi-phase flow rates using sensor measurements located in electrical submersible pumped wells. An exhaustive exploratory data analysis is conducted, including a univariate study of the target outputs (liquid rate and water cut), a multivariate study of the relationships between inputs and outputs, and data grouping based on principal component projections and clustering algorithms. Feature prioritization experiments are performed to identify the most influential parameters in the prediction of flow rates. Model comparison is done using the mean absolute error, mean squared error and coefficient of determination. The results indicate that the CNN-LSTM network architecture is particularly effective in time series analysis for ESP sensor data, as the 1D-CNN layers are capable of extracting features and generating informative representations of time series data automatically. Subsequently, the study presented herein a methodology for implementing predictive maintenance on artificial lift systems, specifically regarding the maintenance of Electrical Submersible Pumps (ESPs). Conventional maintenance practices for ESPs require extensive resources and manpower and are often initiated through reactive monitoring of multivariate sensor data. To address this issue, the study employs the use of principal component analysis (PCA) and extreme gradient boosting trees (XGBoost) to analyze real-time sensor data and predict potential failures in ESPs. PCA is utilized as an unsupervised technique and its output is further processed by the XGBoost model for prediction of system status. The resulting predictive model has been shown to provide signals of potential failures up to seven days in advance, with an F1 score greater than 0.71 on the test set. In addition to the data-driven modeling approach, The present study also in- corporates model-free reinforcement learning (RL) algorithms to aid in decision-making in production optimization. The task of determining the optimal injection strategy poses challenges due to the complexity of the underlying dynamics, including nonlinear formulation, temporal variations, and reservoir heterogeneity. To tackle these challenges, the problem was reformulated as a Markov decision process and RL algorithms were employed to determine actions that maximize production yield. The results of the study demonstrate that the RL agent was able to significantly enhance the net present value (NPV) by continuously interacting with the environment and iteratively refining the dynamic process through multiple episodes. This showcases the potential for RL algorithms to provide effective and efficient solutions for complex optimization problems in the production domain. In conclusion, this study represents an original contribution to the field of data-driven applications in subsurface energy systems. It proposes a data-driven method for determining multi-phase flow rates in electrical submersible pumped (ESP) wells utilizing sensor measurements. The methodology includes conducting exploratory data analysis, conducting experiments to prioritize features, and evaluating models based on mean absolute error, mean squared error, and coefficient of determination. The findings indicate that a convolutional neural network-long short-term memory (CNN-LSTM) network is an effective approach for time series analysis in ESPs. In addition, the study implements principal component analysis (PCA) and extreme gradient boosting trees (XGBoost) to perform predictive maintenance on ESPs and anticipate potential failures up to a seven-day horizon. Furthermore, the study applies model-free reinforcement learning (RL) algorithms to aid decision-making in production optimization and enhance net present value (NPV)

Tracing back the source of contamination

From the time a contaminant is detected in an observation well, the question of where and when the contaminant was introduced in the aquifer needs an answer. Many techniques have been proposed to answer this question, but virtually all of them assume that the aquifer and its dynamics are perfectly known. This work discusses a new approach for the simultaneous identification of the contaminant source location and the spatial variability of hydraulic conductivity in an aquifer which has been validated on synthetic and laboratory experiments and which is in the process of being validated on a real aquifer

Population-based algorithms for improved history matching and uncertainty quantification of Petroleum reservoirs

In modern field management practices, there are two important steps that shed light on a multimillion dollar investment. The first step is history matching where the simulation model is calibrated to reproduce the historical observations from the field. In this inverse problem, different geological and petrophysical properties may provide equally good history matches. Such diverse models are likely to show different production behaviors in future. This ties the history matching with the second step, uncertainty quantification of predictions. Multiple history matched models are essential for a realistic uncertainty estimate of the future field behavior. These two steps facilitate decision making and have a direct impact on technical and financial performance of oil and gas companies. Population-based optimization algorithms have been recently enjoyed growing popularity for solving engineering problems. Population-based systems work with a group of individuals that cooperate and communicate to accomplish a task that is normally beyond the capabilities of each individual. These individuals are deployed with the aim to solve the problem with maximum efficiency. This thesis introduces the application of two novel population-based algorithms for history matching and uncertainty quantification of petroleum reservoir models. Ant colony optimization and differential evolution algorithms are used to search the space of parameters to find multiple history matched models and, using a Bayesian framework, the posterior probability of the models are evaluated for prediction of reservoir performance. It is demonstrated that by bringing latest developments in computer science such as ant colony, differential evolution and multiobjective optimization, we can improve the history matching and uncertainty quantification frameworks. This thesis provides insights into performance of these algorithms in history matching and prediction and develops an understanding of their tuning parameters. The research also brings a comparative study of these methods with a benchmark technique called Neighbourhood Algorithms. This comparison reveals the superiority of the proposed methodologies in various areas such as computational efficiency and match quality

Advancing Carbon Sequestration through Smart Proxy Modeling: Leveraging Domain Expertise and Machine Learning for Efficient Reservoir Simulation

Geological carbon sequestration (GCS) offers a promising solution to effectively manage extra carbon, mitigating the impact of climate change. This doctoral research introduces a cutting-edge Smart Proxy Modeling-based framework, integrating artificial neural networks (ANNs) and domain expertise, to re-engineer and empower numerical reservoir simulation for efficient modeling of CO2 sequestration and demonstrate predictive conformance and replicative capabilities of smart proxy modeling. Creating well-performing proxy models requires extensive human intervention and trial-and-error processes. Additionally, a large training database is essential to ANN model for complex tasks such as deep saline aquifer CO2 sequestration since it is used as the neural network\u27s input and output data. One major limitation in CCS programs is the lack of real field data due to a lack of field applications and issues with confidentiality. Considering these drawbacks, and due to high-dimensional nonlinearity, heterogeneity, and coupling of multiple physical processes associated with numerical reservoir simulation, novel research to handle these complexities as it allows for the creation of possible CO2 sequestration scenarios that may be used as a training set. This study addresses several types of static and dynamic realistic and practical field-base data augmentation techniques ranging from spatial complexity, spatio-temporal complexity, and heterogeneity of reservoir characteristics. By incorporating domain-expertise-based feature generation, this framework honors precise representation of reservoir overcoming computational challenges associated with numerical reservoir tools. The developed ANN accurately replicated fluid flow behavior, resulting in significant computational savings compared to traditional numerical simulation models. The results showed that all the ML models achieved very good accuracies and high efficiency. The findings revealed that the quality of the path between the focal cell and injection wells emerged as the most crucial factor in both CO2 saturation and pressure estimation models. These insights significantly contribute to our understanding of CO2 plume monitoring, paving the way for breakthroughs in investigating reservoir behavior at a minimal computational cost. The study\u27s commitment to replicating numerical reservoir simulation results underscores the model\u27s potential to contribute valuable insights into the behavior and performance of CO2 sequestration systems, as a complimentary tool to numerical reservoir simulation when there is no measured data available from the field. The transformative nature of this research has vast implications for advancing carbon storage modeling technologies. By addressing the computational limitations of traditional numerical reservoir models and harnessing the synergy between machine learning and domain expertise, this work provides a practical workflow for efficient decision-making in sequestration projects